Find the following probabilities. It may help to sketch the pdf for Standard Nor

Question

Find the following probabilities. It may help to sketch the pdf for Standard Normal Distribution and shade in the area that corresponds to the probability of interest.

1) Z~Norm(0,1),findPr(Z1.78)-12pt

2) Z~Norm(0,1),findPr(Z>1.96)-1pt

3) Z~Norm(0,1),findPr(-2.34Z<1.45)-1pt

4) Z ~ Norm(0, 1), find Pr(Z < -0.67) - 12 pt

5) Z ~ Norm(0, 1), find Pr(Z -2.98) - 1 pt

Do the same for the following below. Note however that they are no longer Standard Normal Distributions.

6) X ~ Norm(266, 16^2), find Pr(X < 200) - 1 pt

7) X~Norm(-2,5^2),findPr(-4 70) - 1.25 pt

8) X ~ Norm(64.4, 2.4^2), find Pr(X > 70) - 1.25 pt

Explanation / Answer

HERE THE DISTRIBUTION IS NORMAL

THE FORMULA TO BE USED = Z = (X-MEAN)/STANDARD DEVIATION

1)Z~Norm(0,1),findPr(Z1.78)

P(Z<= 1.78) = THE VALUE TO BE TAKEN FROM THE Z TABLE

= 0.9625

2) P(Z>1.96) = 1 - P(Z=1.96

= 1-0.9750 = 0.250

3)Pr(-2.34Z<1.45)

= P(Z= 1.45) - P(Z = -2.34)

= 0.9265 - 0.0096

= 0.9169

4) P(Z<-0.67)

= VALUE FROM Z TABLE

= 0.2514

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